@article {1251,
	title = {LEARNERS{\textquoteright} VIEWS ON ASYMPTOTES OF A HYPERBOLA AND EXPONENTIAL FUNCTION: A COMMOGNITIVE APPROACH},
	journal = {Problems of Education in the 21st Century},
	volume = {77},
	year = {2019},
	month = {December/2019},
	pages = {Continuous},
	type = {Original article},
	chapter = {734-744},
	abstract = {Learners in South African schools often respond poorly in questions related to the asymptote. Despite the fact that there are only a few functions in the South African curriculum that actually explore the asymptote, learners still show some deficiency in their understanding of the concept. This research examined Grade 11 learners{\textquoteright} mathematical discourses about the asymptotes of the hyperbola and exponential functions. Data were analysed using the Realisation Tree of a Function, an adaptation of the Realisation Tree Assessment tool from Weingarden, Heyd-Metzuyanim and Nachlieli. While the Realisation Tree Assessment tool focused on teacher talk, the Realisation Tree of a Function focused on learner expression and responses. 
A qualitative research design was essentially adopted, with exploratory, descriptive and interpretive elements complementing both its data collection and analysis. A purposive sampling strategy was implemented. Data were collected by means of a test administered to a total of 112 Grade 11 participants from four selected secondary schools. Focus group interviews were conducted with 24 of the best-performing participants by using their responses from the written mathematical tests. 
The results revealed that the learners{\textquoteright} mathematical discourse is not coherent. While learners{\textquoteright} work on each representation was often mathematical there seemed to be a struggle when the task had an unusual orientation. Different expressions of the same mathematical object elicited different responses. The challenge is that learners exhibited a fragmented relationship between the mathematical objects of the function.
},
	keywords = {commognition, realization tree, ritualised learning, visual mediators},
	issn = {1822-7864},
	doi = {https://doi.org/10.33225/pec/19.77.734},
	url = {http://oaji.net/articles/2019/457-1575642547.pdf},
	author = {Vimolan Mudaly and Sihlobosenkosi Mpofu}
}
